canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real number φ − 3/2 built from the RS golden ratio. It is the fixed numerical cutoff packaged in the eight-tick forcing module. Anyone comparing domain costs to a canonical scale cites it. The body is a one-line arithmetic definition in φ.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by self-similarity in Recognition Science.
background
Recognition Science forces a unique dimensionless scale φ (the golden ratio) as the self-similar fixed point of the cost functional (forcing step T6). Constants live in RS-native units with φ imported from the Constants module; the Cost module supplies the underlying J-cost whose fixed-point analysis yields φ.
This file is Foundation RS Module 2: structural theorems on the eight-tick recognition cycle of period $2^D = 2^3 = 8$, forced once spatial dimension is D = 3. The threshold is a pure real built from φ and sits in the same namespace as the domain-cost helpers that will later be compared against it.
proof idea
Definitional. The real is introduced by the arithmetic expression φ − 3/2; there is no proof body, no tactic, and no lemma application.
why it matters
Supplies the numerical cutoff used inside the eight-tick octave package (forcing landmarks T7 and T8). Sibling lemmas such as positivity of the threshold sit immediately downstream in the same module and turn the bare real into a usable comparison scale for domain costs. It does not itself close any open forcing step; it is scaffolding infrastructure for cost-threshold arguments in the RS chain.
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